/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_mat_mult_fast_q31.c
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* Description: Q31 matrix multiplication (fast variant)
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*
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* $Date: 18. March 2019
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* $Revision: V1.6.0
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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/**
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@ingroup groupMatrix
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*/
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/**
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@addtogroup MatrixMult
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@{
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*/
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/**
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@brief Q31 matrix multiplication (fast variant).
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@param[in] pSrcA points to the first input matrix structure
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@param[in] pSrcB points to the second input matrix structure
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@param[out] pDst points to output matrix structure
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@return execution status
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- \ref ARM_MATH_SUCCESS : Operation successful
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- \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed
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@par Scaling and Overflow Behavior
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The difference between the function \ref arm_mat_mult_q31() and this fast variant is that
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the fast variant use a 32-bit rather than a 64-bit accumulator.
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The result of each 1.31 x 1.31 multiplication is truncated to
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2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30
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format. Finally, the accumulator is saturated and converted to a 1.31 result.
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@par
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The fast version has the same overflow behavior as the standard version but provides
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less precision since it discards the low 32 bits of each multiplication result.
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In order to avoid overflows completely the input signals must be scaled down.
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Scale down one of the input matrices by log2(numColsA) bits to avoid overflows,
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as a total of numColsA additions are computed internally for each output element.
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@remark
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Refer to \ref arm_mat_mult_q31() for a slower implementation of this function
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which uses 64-bit accumulation to provide higher precision.
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*/
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arm_status arm_mat_mult_fast_q31(
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const arm_matrix_instance_q31 * pSrcA,
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const arm_matrix_instance_q31 * pSrcB,
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arm_matrix_instance_q31 * pDst)
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{
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q31_t *pInA = pSrcA->pData; /* Input data matrix pointer A */
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q31_t *pInB = pSrcB->pData; /* Input data matrix pointer B */
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q31_t *pInA2;
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q31_t *px; /* Temporary output data matrix pointer */
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q31_t *px2;
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q31_t sum1, sum2, sum3, sum4; /* Accumulator */
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q31_t inA1, inA2, inB1, inB2;
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uint16_t numRowsA = pSrcA->numRows; /* Number of rows of input matrix A */
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uint16_t numColsB = pSrcB->numCols; /* Number of columns of input matrix B */
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uint16_t numColsA = pSrcA->numCols; /* Number of columns of input matrix A */
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uint32_t col, i = 0U, j, row = numRowsA, colCnt; /* Loop counters */
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arm_status status; /* Status of matrix multiplication */
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#ifdef ARM_MATH_MATRIX_CHECK
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/* Check for matrix mismatch condition */
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if ((pSrcA->numCols != pSrcB->numRows) ||
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(pSrcA->numRows != pDst->numRows) ||
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(pSrcB->numCols != pDst->numCols) )
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{
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/* Set status as ARM_MATH_SIZE_MISMATCH */
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status = ARM_MATH_SIZE_MISMATCH;
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}
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else
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#endif /* #ifdef ARM_MATH_MATRIX_CHECK */
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{
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px = pDst->pData;
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row = row >> 1U;
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px2 = px + numColsB;
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/* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
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/* row loop */
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while (row > 0U)
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{
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/* For every row wise process, column loop counter is to be initiated */
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col = numColsB;
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/* For every row wise process, pIn2 pointer is set to starting address of pSrcB data */
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pInB = pSrcB->pData;
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j = 0U;
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col = col >> 1U;
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/* column loop */
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while (col > 0U)
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{
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/* Set the variable sum, that acts as accumulator, to zero */
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sum1 = 0;
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sum2 = 0;
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sum3 = 0;
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sum4 = 0;
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/* Initiate data pointers */
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pInA = pSrcA->pData + i;
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pInB = pSrcB->pData + j;
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pInA2 = pInA + numColsA;
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colCnt = numColsA;
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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/* c(m,n) = a(1,1) * b(1,1) + a(1,2) * b(2,1) + .... + a(m,p) * b(p,n) */
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inA1 = *pInA++;
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inB1 = pInB[0];
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inA2 = *pInA2++;
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inB2 = pInB[1];
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(inA1, inB1, sum1);
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sum2 = __SMMLA(inA1, inB2, sum2);
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sum3 = __SMMLA(inA2, inB1, sum3);
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sum4 = __SMMLA(inA2, inB2, sum4);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) inA1 * inB1)) >> 32);
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sum2 = (q31_t) ((((q63_t) sum2 << 32) + ((q63_t) inA1 * inB2)) >> 32);
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sum3 = (q31_t) ((((q63_t) sum3 << 32) + ((q63_t) inA2 * inB1)) >> 32);
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sum4 = (q31_t) ((((q63_t) sum4 << 32) + ((q63_t) inA2 * inB2)) >> 32);
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#endif
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/* Decrement loop counter */
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colCnt--;
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}
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/* Convert the result from 2.30 to 1.31 format and store in destination buffer */
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*px++ = sum1 << 1;
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*px++ = sum2 << 1;
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*px2++ = sum3 << 1;
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*px2++ = sum4 << 1;
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j += 2;
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/* Decrement column loop counter */
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col--;
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}
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i = i + (numColsA << 1U);
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px = px2 + (numColsB & 1U);
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px2 = px + numColsB;
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/* Decrement row loop counter */
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row--;
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}
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/* Compute any remaining odd row/column below */
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/* Compute remaining output column */
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if (numColsB & 1U) {
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/* Avoid redundant computation of last element */
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row = numRowsA & (~1U);
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/* Point to remaining unfilled column in output matrix */
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px = pDst->pData + numColsB-1;
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pInA = pSrcA->pData;
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/* row loop */
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while (row > 0)
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{
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/* point to last column in matrix B */
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pInB = pSrcB->pData + numColsB-1;
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/* Set variable sum1, that acts as accumulator, to zero */
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sum1 = 0;
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#if defined (ARM_MATH_LOOPUNROLL)
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/* Loop unrolling: Compute 4 columns at a time. */
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colCnt = numColsA >> 2U;
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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/* Decrement loop counter */
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colCnt--;
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}
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/* Loop unrolling: Compute remaining column */
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colCnt = numColsA % 4U;
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#else
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/* Initialize colCnt with number of columns */
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colCnt = numColsA;
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#endif /* #if defined (ARM_MATH_LOOPUNROLL) */
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while (colCnt > 0U) {
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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colCnt--;
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}
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/* Convert the result from 2.30 to 1.31 format and store in destination buffer */
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*px = sum1 << 1;
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px += numColsB;
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/* Decrement row loop counter */
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row--;
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}
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}
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/* Compute remaining output row */
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if (numRowsA & 1U) {
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/* point to last row in output matrix */
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px = pDst->pData + (numColsB) * (numRowsA-1);
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col = numColsB;
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i = 0U;
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/* col loop */
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while (col > 0)
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{
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/* point to last row in matrix A */
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pInA = pSrcA->pData + (numRowsA-1) * numColsA;
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pInB = pSrcB->pData + i;
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/* Set variable sum1, that acts as accumulator, to zero */
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sum1 = 0;
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#if defined (ARM_MATH_LOOPUNROLL)
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/* Loop unrolling: Compute 4 columns at a time. */
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colCnt = numColsA >> 2U;
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/* matrix multiplication */
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while (colCnt > 0U)
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{
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inA1 = *pInA++;
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inA2 = *pInA++;
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inB1 = *pInB;
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pInB += numColsB;
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inB2 = *pInB;
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(inA1, inB1, sum1);
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sum1 = __SMMLA(inA2, inB2, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) inA1 * inB1)) >> 32);
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) inA2 * inB2)) >> 32);
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#endif
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inA1 = *pInA++;
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inA2 = *pInA++;
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inB1 = *pInB;
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pInB += numColsB;
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inB2 = *pInB;
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pInB += numColsB;
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(inA1, inB1, sum1);
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sum1 = __SMMLA(inA2, inB2, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) inA1 * inB1)) >> 32);
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) inA2 * inB2)) >> 32);
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#endif
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/* Decrement loop counter */
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colCnt--;
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}
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/* Loop unrolling: Compute remaining column */
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colCnt = numColsA % 4U;
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#else
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/* Initialize colCnt with number of columns */
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colCnt = numColsA;
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#endif /* #if defined (ARM_MATH_LOOPUNROLL) */
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while (colCnt > 0U) {
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#if defined (ARM_MATH_DSP)
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sum1 = __SMMLA(*pInA++, *pInB, sum1);
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#else
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sum1 = (q31_t) ((((q63_t) sum1 << 32) + ((q63_t) *pInA++ * *pInB)) >> 32);
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#endif
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pInB += numColsB;
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colCnt--;
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}
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/* Saturate and store the result in the destination buffer */
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*px++ = sum1 << 1;
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i++;
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/* Decrement col loop counter */
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col--;
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}
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}
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/* Set status as ARM_MATH_SUCCESS */
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status = ARM_MATH_SUCCESS;
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}
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/* Return to application */
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return (status);
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}
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/**
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@} end of MatrixMult group
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*/
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